Regularity properties of tug-of-war games and normalized equations
Julkaistu sarjassa
Report / University of Jyväskylä, Department of Mathematics and StatisticsTekijät
Päivämäärä
2017Oppiaine
MatematiikkaJulkaisija
University of JyväskyläISBN
978-951-39-7026-0ISSN Hae Julkaisufoorumista
1457-8905Asiasanat
Metadata
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- Väitöskirjat [3524]
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On the local and global regularity of tug-of-war games
Heino, Joonas (University of Jyväskylä, 2018)This thesis studies local and global regularity properties of a stochastic two-player zero-sum game called tug-of-war. In particular, we study value functions of the game locally as well as globally, that is, close to ... -
Uniform measure density condition and game regularity for tug-of-war games
Heino, Joonas (International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2018)We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for ... -
Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
Arroyo Garcia, Angel; Luiro, Hannes; Parviainen, Mikko; Ruosteenoja, Eero (Springer, 2020)We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ⊂ ℝn. The method of the proof is based on a game-theoretic idea to estimate the value of a related ... -
Local regularity estimates for general discrete dynamic programming equations
Arroyo, Ángel; Blanc, Pablo; Parviainen, Mikko (Elsevier, 2022)We obtain an analytic proof for asymptotic Hölder estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for ... -
Gradient and Lipschitz Estimates for Tug-of-War Type Games
Attouchi, Amal; Luiro, Hannes; Parviainen, Mikko (Society for Industrial and Applied Mathematics, 2021)We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the ...
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